Question: Simplify the following expression: $ x = \dfrac{-5}{3} - \dfrac{4p - 10}{-3p} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-3p}{-3p}$ $ \dfrac{-5}{3} \times \dfrac{-3p}{-3p} = \dfrac{15p}{-9p} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{4p - 10}{-3p} \times \dfrac{3}{3} = \dfrac{12p - 30}{-9p} $ Therefore $ x = \dfrac{15p}{-9p} - \dfrac{12p - 30}{-9p} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{15p - (12p - 30) }{-9p} $ Distribute the negative sign: $x = \dfrac{15p - 12p + 30}{-9p}$ $x = \dfrac{3p + 30}{-9p}$ Simplify the expression by dividing the numerator and denominator by -3: $x = \dfrac{-p - 10}{3p}$